# Large monochromatic components of small diameter

@article{Carlson2022LargeMC, title={Large monochromatic components of small diameter}, author={Erik Carlson and Ryan R. Martin and Bo Peng and Mikl'os Ruszink'o}, journal={J. Graph Theory}, year={2022}, volume={99}, pages={247-250} }

Gyárfás [4] conjectured in 2011 that every r-edge-colored Kn contains a monochromatic component of bounded (“perhaps three”) diameter on at least n/(r−1) vertices. Letzter [6] proved this conjecture with diameter four. In this note we improve the result in the case of r = 3: We show that in every 3-edge-coloring of Kn either there is a monochromatic component of diameter at most three on at least n/2 vertices or every color class is spanning and has diameter at most four. 1 Monochromatic…

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